Anti-rolling structure for box-type floating body

ABSTRACT

A floating body  1,  which is substantially rectangular when seen from above, is provided with at least a protrusion  3  on at least either of sides in a transverse direction  5  of the floating body  1  at a level lower than a waterline  4.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to an anti-rolling structure for abox-type floating body such as a hull of a work-ship or -vessel or ahull for FPSO (Floating Production, Storage and Off-Loading).

[0002] In recent years, various new types of active anti-rolling systemsfor reducing roll motion of a hull in waves have been studied and someof them are already in practical use. Active anti-rolling systems areevidently superior to passive ones in terms of their roll reducingeffect.

[0003] However, various active anti-rolling systems for reducing rollmotion of hulls are generally complicated in structure, large-sized andheavy-weighted and require a large installation space. For reasons ofeconomy and space, such systems are usually difficult to adopt forhulls.

[0004] Then, studies have been consequently made on passive anti-rollingsystems which reduce roll motion by devising specifications and forms ofhulls. A result of such studies was published in the bulletin of theKansai Society of Naval Architects, extra volume with issue number 232(September 1999). “Several studies on reducing roll motion in waves” (pp63-70) is a paper of studies published in this bulletin. According tothe paper, roll motion of box-type floating bodies can be reduced byadjusting height of the center of gravity. The content of the paper isnow referred to below.

[0005]FIG. 1 shows an example of a box-type floating body 1 seen fromthe rear. The floating body 1 has a breadth B and a draft d. A center Gof gravity of the floating body 1 is located near an origin O at which awaterline lies, or for example, a little above the origin O.

[0006] When the box-type floating body 1 as described above is subjectedto beam seas, rolling motion 2 is generated which acts to rotate thefloating body 1 around the center G of gravity.

[0007] The paper studies on reduction of roll motion of the box-typefloating body 1 having a large ratio of the breadth B to the draft d (alarge breadth/draft ratio) and argues that the roll motion can bereduced by shifting the position of the center G of gravity of thefloating body 1.

[0008] Theoretical foundation of the study is an equation of motion withone degree of freedom for roll motion (rolling) having a synchronousinfluence on sway motion (swaying). Here the sway motion means a motionin which the box-type floating body 1 horizontally moves to right andleft; and the roll motion, a motion in which the floating body 1rotationally moves around the center G of gravity. An equation of motionwith one degree of freedom, which is expressed in a more simple form, isuseful in estimating a possibility of the reduction of roll motion.

[0009] An equation of motion with one degree of freedom for roll motionin which simultaneousness of the sway and rolling motions is consideredis given as follows from an equation of synchronized motion of rollingand swaying: $\begin{matrix}{{\left\lbrack {D_{4} - \frac{D_{24}^{2}}{D_{2}}} \right\rbrack \frac{X_{4}}{\zeta_{A}}} = {H_{4} - {\frac{D_{24}}{D_{2}}H_{2}}}} & (1)\end{matrix}$

[0010] where X₄ is an amplitude of the roll motion; H_(j) (j=2, 4), theKochin function; D_(j) and D₂₄, coefficients that depend on hydrodynamicforce; and j=2 and 4, the sway motion and the roll motion, respectively.

[0011] The right-hand side of Equation (1) is the wave exciting momentof roll motion in a broad sense, which includes influence from the swaymotion. A relationship is formed as the equation below between the waveexciting moment of roll motion and effective wave slope coefficient γ:$\begin{matrix}{{{\gamma \cdot G}\quad M} = {{- i}\frac{H_{4} - {\left( {D_{24}/D_{2}} \right)H_{2}}}{K{\nabla{/\left( {B/2} \right)}}}}} & (2)\end{matrix}$

[0012] Next, define an added mass coefficient k₂ of sway motion,hydrodynamic force lever l₂ and wave exciting moment lever l_(w), giving$\begin{matrix}\left. \begin{matrix}{\quad {k_{2} = {{m_{22}/\rho}\nabla}}} \\{\quad {l_{2} = {{- m_{24}}/m_{22}}}} \\{\quad {{l_{w}/\left( {B/2} \right)} = {{- H_{4}}/H_{2}}}}\end{matrix} \right\} & (3)\end{matrix}$

[0013] where l₂ and l_(w) are distances measured from the center G ofgravity of the box-type floating body 1 to the points where respectiveforces act and are defined as positive toward upwards.

[0014] With l₂₀ and l_(wo) as moment levers being defined about theorigin O, giving

l(K)=k ₂ l ₂₀−(1+k ₂)l _(wo)   (4)

[0015] When

γs=(i/k∇){H ₂/(1+k ₂)}  (5)

[0016] holds, Equation (2) can be rewritten as

γ·GM=γ s{OG−l (K)}  (6),

[0017] where OG is distance from the origin O lying at the waterline tothe center G of gravity and is defined as positive when the center G ofgravity is located below the origin O; GM is height of the metacenter M(the distance from the center G of gravity to the metacenter M).

[0018] γ s corresponds to an approximate value of the amplitude ofsingle sway motion, and a moment lever l(K) is a value independent ofthe location of the center of gravity. Both γ s and l(K) depend on theshape and motion frequency of the box-type floating body 1.

[0019] γ s, a component of an effective wave slope coefficient, and themoment lever l(K) were calculated on the box-type floating body 1. Thefloating body 1 on which the calculations are made has six differentvalues of B/d: 2.5, 5, 7.5, 10, 12.5 and 20. The two-dimensionalvelocity potential continuation method is used for calculation in whichthree-dimensional influence on a hydrodynamic force is not considered.

[0020] Calculated values of γ s are shown in FIG. 2. The abscissa inFIG. 2 represents a non-dimensional frequency K(B/2) where K=ω²/g,ω=2π/T, and ω and T are a frequency and wave period, respectively.

[0021] As shown in FIG. 2, γ s flatly decreases as the frequencyincreases. γ s changes a little with a change in the breadth/draft ratioof the box-type floating body 1; in shallow-draft box-type floatingbodies having a B/d ratio of 5 or more, the values of γ s may beregarded as similar.

[0022]FIG. 3 shows the relationship between the ratio of the momentlever l(K) to a half-breadth B/2, or l(K)/(B/2) (the ordinate), and thenon-dimensional frequency K(B/2) (the abscissa) with B/d as a parameter.l(K)/(B/2) varies slightly against the frequency, but variesconsiderably with the breadth/draft ratio. The greater the B/d, thegreater the absolute value of l(K)/(B/2). With B/d=5, l(K)/(B/d) isnearly zero, showing substantially no change against the frequency. Thevalue of l(K) is obtainable from FIG. 3 if both the breadth/draft ratioB/d and the wave frequency of a sea area where the floating structure isinstalled are given.

[0023] There are three fundamental ideas to reduce the motion of abox-type floating body in waves: increase in damping force, prolongationof the natural period of the motion and reduction in the wave excitingforce. In the equation (1) of synchronized motion, reducing the waveexciting force means to make smaller the value of the right-hand side,which can be achieved by making γ·GM smaller as can be seen fromEquation (2). Since γ·GM can be expressed as Equation (6), γ·GM=0 eitherwhen γ s=0 at a certain frequency or when OG=l(K). In this paperreduction in roll motion is realized with this idea.

[0024] First, H₂(K)=0 is needed in order to have γ s=0, which istheoretically achievable by selecting the shape of a floating body whichhas no sway waves. However, realistic shapes may not be obtainable forbox-type floating bodies having larger breadth/draft ratios.

[0025] On the other hand, OG=l(K) may be achieved depending on theheight OG of the center of gravity. Although it has been conventionallysaid that obtaining OG=l(K) is difficult for sea areas with relativelylong wave lengths, such a case applies to ships with a general shape;and it is obtainable in box-type floating bodies having largebreadth/draft ratios.

[0026] Realizing OG=l(K) through adjustment of the OG value may beachieved by, for example, making OG larger by installing a base on thebox-type floating body to mount a heavy object on it. However, when OGis made larger, the value of GM becomes smaller, which may make thefloating body unstable depending on its shape.

[0027] The present invention was made in view of the above and has itsobject to provide an anti-rolling structure for box-type floating bodiesin which shapes of the box-type floating bodies are modified to adjust avalue of moment lever l(K), thereby attaining OG=l(K) to reduce the waveexciting force.

BRIEF SUMMARY OF THE INVENTION

[0028] In order to solve the above-mentioned problems, the presentinvention provides an anti-rolling structure for a box-type floatingbody comprising said floating body which is substantially rectangularwhen seen from above and at least a protrusion on at least either oftransverse sides of the floating body, said protrusion extendinglongitudinally of the floating body at a level lower than a waterline.

[0029] Preferably, said longitudinal protrusion extends oversubstantially an entire length of the floating body.

[0030] Said longitudinal protrusion may extend partially of the floatingbody.

[0031] Preferably, in addition to the longitudinal protrusion at thelevel lower than the waterline, a plurality of vertical protrusions arearranged on the floating body and are spaced apart from each otherlongitudinally of the floating body, each of said vertical protrusionshaving a protruded dimension substantially equal to that of thelongitudinal protrusion.

[0032] Preferably, the longitudinal protrusion is shaped such thatheight of center of gravity of the floating body substantially coincideswith a moment lever acting on the floating body.

[0033] Preferably, the longitudinal protrusion is at a lower edge of thebox-type floating body.

[0034] An operation of the invention will be described. A moment leverl(K) acting on a floating body, which depends on different factors suchas an added mass synchronous coefficient of sway motion of the floatingbody and wave exciting force, can be obtained, as explained with FIG. 3,from the graph when the frequency is given with the breadth/draft ratioB/d as a parameter. With respect to an average frequency or period ofwaves in a sea area in which a floating body such as a hull of awork-ship or a hull for FPSO is installed, a value of the moment leverl(K) thus obtained does not usually coincide with height OG of thecenter of gravity except accidental coincidence. The value of OG may beadjusted to make it have the same value as or close to that of themoment lever, but such a way is not always practical. In the presentinvention, at least a longitudinal protrusion is provided on at leasteither of transverse sides of a box-type floating body at a level lowerthan a waterline to thereby adjust the moment lever l(K) to a value sameas or close to that of OG. As a result, the wave exciting force isreduced for less roll motion of the box-type floating body.

BRIEF DESCRIPTION OF THE DRAWINGS

[0035]FIG. 1 shows a rear view of a conventional box-type floating body;

[0036]FIG. 2 is a graph showing the relationship between γ s andnon-dimensional frequency of the conventional box-type floating body;

[0037]FIG. 3 is a graph showing the relationship between a moment leverl(K) and non-dimensional frequency of the conventional box-type floatingbody;

[0038]FIGS. 4A, 4B and 4C show side, plan and front views of ananti-rolling structure for a box-type floating body in accordance withthe present invention, respectively;

[0039]FIG. 5 shows a vertical section of a hull for FPSO taken at thecenter in the longitudinal direction;

[0040]FIG. 6 is a graph showing the relationship between the momentlever and frequency of the floating body shown in FIG. 5;

[0041]FIGS. 7A and 7B are graphs showing roll reducing effect when B_(s)is varied from 0 through 4 m in the floating body shown in FIG. 5, theformer representing the relationship between the roll response functionand wave period and the latter representing the relationship between aresult of the roll short-term assumption and average wave period;

[0042]FIG. 8 is a graph showing, with respect to the floating body shownin FIG. 5, the relationship between the number of non-operation days ayear and roll angle of the floating body at which operation is stopped;

[0043]FIGS. 9A, 9B and 9C show side, plan and front views of amodification of an anti-rolling structure for a box-type floating bodyin accordance with the invention, respectively;

[0044]FIGS. 10A, 10B and 10C show side, plan and front views of afurther modification of an anti-rolling structure for a box-typefloating body in accordance with the invention, respectively;

[0045]FIGS. 11A, 11B and 11C show side, plan and front views of a stillfurther modification of an anti-rolling structure for a box-typefloating body in accordance with the invention, respectively;

[0046]FIG. 12 is a perspective view showing the still furthermodification with a ship or vessel being brought alongside the floatingbody; and

[0047]FIG. 13 is a graph showing roll reducing effect of the box-typefloating body shown in FIG. 5, where Bs is set at 4 m and summed totallength of the protrusions is ½ of, ⅔ of, and equal to the overall lengthof the floating body, representing the relationship between the rollresponse function and wave period.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0048] An embodiment of the invention will be described with referenceto the accompanying drawings. FIGS. 4A, 4B and 4C are side, plan andfront views of an anti-rolling structure for a box-type floating body inaccordance with the invention, respectively. Reference numerals same asthose in FIG. 1 are used to designate similar parts throughout thefigures. In the figures, reference numeral 1 denotes a box-type floatingbody of a work-ship or for FPSO. The floating body 1 is rectangular whenseen from above and has a flat bottom. Protrusions 3 are attached toboth sides in a transverse direction 5 of the floating body 1; andextend substantially over the entire length in a longitudinal direction6 of the floating body 1 at a level lower than a waterline 4. Theprotrusions 3 in the figures are shown to be at lower edges of thefloating body 1; they may be, however, arranged at positions other thanthe lower edges.

[0049] Preferably, the protrusions 3 are shaped such that height OG ofcenter of gravity of the floating body substantially coincides with themoment lever l(K) acting on the floating body.

[0050] Next, a result of calculations for a specific example will bedescribed. FIG. 5 is a view showing a transverse section, taken at thecenter in the longitudinal direction, of a hull for FPSO under planning;this is presented as a specific example of the anti-rolling structure ofthe invention. The FPSO hull has a length of 295 m, a breadth B of 60 mand a height D of 25 m. The draft depth d is 9 m for a case withoutprotrusions, and 8.47 m for a case with protrusions of the maximumprotruded dimension. The height OG of the center of the gravity is −8.16m, where OG is negative when G is located above a water surface O. Thus,OG/(B/2)=−0.272 is obtained. The calculations were made with thedifferent protruding dimension Bs: Bs=0, Bs=1 m, Bs=2 m, Bs=3 m, andBs=4 m.

[0051] Since the average wave period in a sea area where the box-typefloating body 1 is planned to be installed is 10 sec, it is so arrangedthat the maximum roll reducing effect should be obtained at this waveperiod. FIG. 6 is a graph showing the relationship between the ratio ofthe moment lever l(K) to a half-breadth B/2, or l(K)/(B/2) (theordinate) and non-dimensional frequency K(B/2) (the abscissa) of thebox-type floating body (B/d=6.67) shown in FIG. 5. The dashed linedenotes Bs=0, a box-type floating body without the protrusions 3, andthe continuous line denotes the graph for a box-type floating body withthe protrusions 3 having Bs=4 m. When T=10 sec, K(B/2)=1.2, and, asunderstood from FIG. 6, l(K)/(B/2) is approximately −0.45 in a box-typefloating body having Bs=0. With the protrusions 3 having Bs=4,l(K)/(B/2) becomes −0.272 for the average wave period of 10 sec, andthus OG=l(K) is realized.

[0052]FIG. 7A is a graph showing roll reducing effect when Bs is variedfrom 0 through 4, representing the relationship between the rollresponse function and wave period. FIG. 7B represents the relationshipbetween a result of the roll short-term assumption and average waveperiod. In the diagrams, Type—0 represents Bs=0; Type-B#1, B =1;Type-B#2, Bs=2; Type-B#3, Bs=3; and Type-B#4, Bs=4. As seen in FIG. 7A,the synchronous period at which the response of roll motion reaches themaximum becomes larger as Bs varies from 0 through 4. It is understoodfrom FIG. 7B that, when the average wave period of an intended sea areaof the installation is 10 sec, roll motion is considerably suppressed bysetting the protrusions 3 as Bs=4 m. Adding protrusions to those usedfor the calculations above can further reduce roll motion since when anincrease in the added mass of roll motion occurs an effect of viscousdamping can also be expected.

[0053]FIG. 8 is a diagram showing the relationship, in oceanographicphenomena in an intended sea area of the installation, between thenumber of non-operation days a year (the ordinate) and roll angle of thefloating body at which operation is stopped (the abscissa), wherein thecases of Bs=0, Bs=2 and Bs=4 are indicated. When the angle at which theoperation of plants, etc. are stopped is set at 5 degrees, conventionalstructures (Bs=0) have about 9 non-operation days a year, while astructure of the present invention (Bs=4) has about 3 non-operation daysa year, showing remarkable improvement.

[0054] Modifications of the invention will be described referring to theaccompanying drawings. FIGS. 9A, 9B and 9C show a modification of theinvention in which longitudinal protrusions extend partially on bothtransverse sides of the box-type floating body 1. Partial longitudinalprotrusions 3 a, each having a length of ⅓ of the overall length of thefloating body, are attached to front and rear portions of the box-typefloating body 1. FIG. 13 is a graph showing the relationship between theroll response function and wave period when the summed length of all thelongitudinal protrusions 3 a is ½ (case 1) of, ⅔ (case 2) of and equal(case 3) to the overall length of the floating body 1 . The protrudeddimension in the drawing is Bs=4. Comparing the case of Bs=4 in FIG. 13with that of Bs=0 in FIG. 7A, it is understood that, in each of thecases 1, 2 and 3 in FIG. 13, the synchronous periods at which rollresponse reaches the maximum is larger than those shown in FIG. 7A. Itis also seen in the same diagram that there is a little differencebetween the case where the summed length of all the protrusions 3 a inthe longitudinal direction is ⅔ of the overall length and the case wherethe summed length is equal to the overall length of the floating body 1.

[0055]FIGS. 10A, 10B and 10C show a further modification of theinvention in which the single longitudinal protrusion 3 is attached onlyto one of the transverse sides of the box-type floating body 1. This isadvantageous when the center G of gravity of the floating body 1 iseccentric.

[0056]FIGS. 11A, 11B and 11C show a still further modification of theinvention in which a plurality of vertical protrusions 7 (5 pieces inthe example), each having an substantially equal protruded dimension Bs,are installed in addition to the longitudinal protrusions 3 at the levellower than the waterline. FIG. 12 is a perspective view showing that avessel 8 is brought alongside the box-type floating body 1.

[0057] When the box-type floating body 1 is provided only with thelongitudinal protrusions 3, the protrusions 3 and the vessel 8 maycollide with each other even if fenders are placed between the vessel 8and the floating body 1 since the vessel 8, which is brought alongsidethe floating body 1, may have roll period and phase different from thoseof the floating body 1. However, when the floating body 1 is providedalso with the vertical protrusions 7 and fenders are attached to theprotrusions 7, the vessel 8 can safely come alongside the floating body1.

[0058] It is to be understood that the present invention is not limitedto the embodiments and modifications described above and that variouschanges and further modifications may be made without deviating from thescope and spirit of the invention. For example, it has been describedthat protrusions are attached to a box-type floating body as additionalobjects; but box-type floating bodies may be formed to have protrusionsintegral therewith. The shapes of the protrusions do not necessarilyneed to achieve OG=l (K). Satisfying required specifications by bringingl(K) closer to OG may also be a solution. Furthermore, the shape of thebox-type floating body is to be substantially rectangular when seen fromabove; both longitudinal ends of the floating body may be a trapezoidalas shown in FIGS. 4A, 4B and 4C or semi-circular shape.

[0059] As described above, the anti-rolling structure for a box-typefloating body according to the invention offers a simple structure withprotrusions below the waterline. It provides an excellent effect toremarkably reduce the roll motion of box-type floating body in anintended sea area of installation.

What is claimed is:
 1. An anti-rolling structure for a box-type floatingbody comprising said floating body which is substantially rectangularwhen seen from above and at least a protrusion on at least either oftransverse sides of the floating body, said protrusion extendinglongitudinally of the floating body at a level lower than a waterline.2. An anti-rolling structure according to claim 1 wherein saidprotrusion extends over substantially an entire length of the floatingbody.
 3. An anti-rolling structure according to claim 1 wherein saidprotrusion extends partially of the floating body.
 4. An anti-rollingstructure according to any one of claims 1 to 3 wherein, in addition tothe longitudinal protrusion at the level lower than the waterline, aplurality of vertical protrusions are arranged on the floating body andare spaced apart from each other longitudinally of the floating body,each of said vertical protrusions having a protruded dimensionsubstantially equal to that of the longitudinal protrusion.
 5. Ananti-rolling structure according to any one of claims 1 to 3 whereinsaid longitudinal protrusion is shaped such that height of center ofgravity of the floating body substantially coincides with a moment leveracting on the floating body.
 6. An anti-rolling structure according toclaim 4 wherein said longitudinal protrusion is shaped such that heightof center of gravity of the floating body substantially coincides with amoment lever acting on the floating body.
 7. An anti-rolling structureaccording to any one of claims 1 to 3 wherein said longitudinalprotrusion is at a lower edge of the floating body.
 8. An anti-rollingstructure according to claim 4 wherein said longitudinal protrusion isat a lower edge of the floating body.
 9. An anti-rolling structureaccording to claim 5 wherein said longitudinal protrusion is at a loweredge of the floating body.